How many measurements does the readout cost?

• What computational problems are worth running on a quantum computer?
• How can keep the lenghth of a quantum computation short?
• How many measurements and hence quantum circuit evaluations does it take?

These questions are critical to obtain a practically relevant quantum advantage. Often, circuit depth and shot count can be traded against each other. We have a strong focus on shot-count reduction but within the [NOGS project] we are also working on reducing the circuit depth for quantum algorithms for spectral properties of quantum chemical systems.

Selected results

• A measurement budget that is provably enough.
  ShadowGrouping decides which Pauli observables to measure next so that a target energy accuracy is reached with a certified number of shots. In numerical benchmarks it needs fewer measurements than previous grouping and shadow-based schemes.
  • Gresch, Kliesch, Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping, [arXiv:2301.03385], Nat. Commun. 16, 689 (2025); presented as a talk at TQC 2023, Aveiro.
• Exploiting the geometry of lattice models
  • Eckstein, Mansuroglu, Wolf, Nützel, Tasler, Kliesch, Hartmann, Shot-noise reduction for lattice Hamiltonians, [arXiv:2410.21251], PRX Quantum 7, 020303 (2026). Presented as a talk at QCTiP 2025, Berlin.
• Letting the experiment tell us how many shots it needs.
  Worst-case bounds are safe but wasteful; we use the variance observed during the run itself to reallocate the remaining budget, which keeps rigorous error bars while spending substantially fewer measurements.
  • Gresch, Tepe, Kliesch, Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information, [arXiv:2502.01730], J. Chem. Theory Comput. 21(15), 7352–7359 (2025).
• Cheaper gradients for variational algorithms.
  Parameter-shift rules evaluate the circuit separately for every parameter; our estimator extracts the same gradient information from considerably fewer circuit evaluations, which directly shortens each optimization step.
  • Bittel, Watty, Kliesch, Fast gradient estimation for variational quantum algorithms, [arXiv:2210.06484], preprint (2022).

Quantum optimization: annealing and QAOA

• Optimization is the application most often claimed for near-term quantum hardware, so this is where the gap between claim and evidence has to be measured most carefully.
  Quantum annealers connect each qubit to only a few others, and the standard minor-embedding fix consumes many physical qubits per logical variable; we develop splitting and linearization techniques that recover usable problem sizes.
  The NP-hardness result above applies directly to QAOA, the variational algorithm proposed for combinatorial optimization: its classical training step is hard even on a perfect device.
  • Seelbach Benkner, Lähner, Golyanik, Kliesch, Moeller, Compensating connectivity restrictions in quantum annealers via splitting and linearization techniques, [arXiv:2507.12536], preprint (2025).
  • Alessandroni et al., Scalable Determination of Penalization Weights for Constrained Optimizations on Approximate Solvers, preprint [arXiv:2604.02416], preprint (2026).

All our publications on this topic

The following search runs live at arXiv, so the list stays current without manual maintenance:
[All our preprints on quantum algorithms and energy estimation (arXiv)].

Funding

Two BMFTR collaborative projects support this work, both aimed at bringing the measurement cost of quantum algorithms down far enough to matter.

• NOGS, Quantum algorithms for chemical ground-state properties without preparing the ground state, 2025 to 2027, with Covestro [project atlas], grant 13N17144). Our subproject covers efficient readout of quantum computers and energy estimation by superresolution methods.
• QUBE, Quantum algorithm development, benchmarking and resource estimation for materials simulation on NISQ computers, 2024 to 2027, with Bosch, Saarland University, Fraunhofer IWM and IQM [project atlas], grant 13N17149). Our subproject covers robust and efficient energy estimation for materials science.